Journal Title/Source
Journal of Algebra
Publication Date
2016
Volume
457
Page Numbers
7-17
Document Type
Journal Article
Department
Mathematics and Computer Science
Abstract
Birkhoff defined a quasigroup as an algebra (Q, ·, \, /) that satisfies the following six identities: x ·(x\y) = y, (y/x)· x = y, x\(x · y) = y, (y · x)/x = y, x/(y\x) = y, and (x/y)\x = y . We investigate triples and tetrads of identities composed of these six, emphasizing those that axiomatize the variety of quasigroups. Key words: (left) quasigroup, (equational) quasigroup, division groupoid, cancellation groupoid 2000 MSC: 20N05
Recommended Citation
Phillips, J.D., "On Birkhoff’s Quasigroup Axioms" (2016). Journal Articles. 518.
https://commons.nmu.edu/facwork_journalarticles/518
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